arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.05614cs.CR
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区块链中自私挖掘的高效MDP分析

Efficient MDP Analysis for Selfish-Mining in Blockchains

Roi Bar-Zur, Ittay Eyal, Aviv Tamar

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摘要：

工作量证明（PoW）区块链协议根据其参与者（称为矿工）在总计算能力中的份额向其分配奖励。足够大的矿工可以执行自私的挖掘-偏离协议以获得超过其公平份额的收益。因此，如果所有矿工都小于阈值大小，那么这样的系统是安全的，因此他们的最佳响应是遵循协议。为了找到阈值，必须确定不同规模的矿工的最佳策略，即，马尔可夫决策过程（MDP）然而，由于PoW难度调整机制，矿工的效用是一个非线性比率函数。因此，我们称之为平均回报率（ARR）MDP。Sapirshtein等人是第一个通过求解一系列收敛到ARR MDP解的标准MDP来求解ARR MDP的人。在这项工作中，我们提出了一种新的技术，通过解决一个标准的MDP解决ARR MDP。我们的方法的关键是增加MDP，使其在预期的轮数内随机终止。我们称之为概率终止优化（PTO），该技术适用于任何效用为比率函数的MDP。我们限制了PTO的近似误差-它与终止前的预期轮数成反比，这是我们控制的参数。从经验上看，PTO的复杂度比现有技术低一个数量级，PTO可以很容易地应用于不同的区块链。我们用它来收紧以太坊中自私挖矿的门槛。

英文摘要：

A proof of work (PoW) blockchain protocol distributes rewards to its participants, called miners, according to their share of the total computational power. Sufficiently large miners can perform selfish mining - deviate from the protocol to gain more than their fair share. Such systems are thus secure if all miners are smaller than a threshold size so their best response is following the protocol. To find the threshold, one has to identify the optimal strategy for miners of different sizes, i.e., solve a Markov Decision Process (MDP). However, because of the PoW difficulty adjustment mechanism, the miners' utility is a non-linear ratio function. We therefore call this an Average Reward Ratio (ARR) MDP. Sapirshtein et al.\ were the first to solve ARR MDPs by solving a series of standard MDPs that converge to the ARR MDP solution. In this work, we present a novel technique for solving an ARR MDP by solving a single standard MDP. The crux of our approach is to augment the MDP such that it terminates randomly, within an expected number of rounds. We call this Probabilistic Termination Optimization (PTO), and the technique applies to any MDP whose utility is a ratio function. We bound the approximation error of PTO - it is inversely proportional to the expected number of rounds before termination, a parameter that we control. Empirically, PTO's complexity is an order of magnitude lower than the state of the art. PTO can be easily applied to different blockchains. We use it to tighten the bound on the threshold for selfish mining in Ethereum.

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